Contents 1 An Outline of What Computational Chemistry Is All About 1 1.1 What You Can Do with Computational Chemistry 1 1.2 The Tools of Computational Chemistry 2 1.3 Putting It All Together 3 1.4 The Philosophy of Computational Chemistry 4 1.5 Summary 5 References 5 Easier Questions 6 Harder Questions 7 2 The Concept of the Potential Energy Surface 9 2.1 Perspective 9 2.2 Stationary Points 13 2.3 The Bom-Oppenheimer Approximation 21 2.4 Geometry Optimization 23 2.5 Stationary Points and Normal-Mode Vibrations—Zero Point Energy 30 2.6 Symmetry 36 2.7 Summary 39 References 40 Easier Questions 42 Harder Questions 42 3 Molecular Mechanics 45 3.1 Perspective 45 3.2 The Basic Principles of Molecular Mechanics 48 3.2.1 Developing a Forcefield 48 3.2.2 Parameterizing a Forcefield 53 3.2.3 A Calculation Using Our Forcefield 57 3.3 Examples of the Use of Molecular Mechanics 3.3.1 To Obtain Reasonable Input Geometries for Lengthier (Ab Initio, Semiempirical or Density Functional) Kinds of Calculations 60 3.3.2 To Obtain Good Geometries (and Perhaps Energies) for Small- to Medium-Sized Molecules 61 3.3.3 To Calculate the Geometries and Energies of Very Large Molecules, Usually Polymeric Biomolecules (Proteins and Nucleic Acids) 64 3.3.4 To Generate the Potential Energy Function Under Which Molecules Move, for Molecular Dynamics or Monte Carlo Calculations 65 3.3.5 As a (Usually Quick) Guide to the Feasibility of, or Likely Outcome of, Reactions in Organic Synthesis 65 3.4 Geometries Calculated by MM 66 3.5 Frequencies and Vibrational Spectra Calculated by MM 67 3.6 Strengths and Weaknesses of Molecular Mechanics 72 3.6.1 Strengths 73 3.6.2 Weaknesses 73 3.7 Summary 74 References 78 Easier Questions 79 Harder Questions 82 4 Introduction to Quantum Mechanics in Computational Chemistry 85 4.1 Perspective 85 4.2 The Development of Quantum Mechanics. The Schrodinger Equation 87 4.2.1 The Origins of Quantum Theory: Blackbody Radiation and the Photoelectric Effect 87 4.2.2 Radioactivity 91 4.2.3 Relativity 91 4.2.4 The Nuclear Atom 92 4.2.5 The Bohr Atom 94 4.2.6 The Wave Mechanical Atom and the Schrodinger Equation 96 4.3 The Application of the Schrodinger Equation to Chemistry by Huckel 102 4.3.1 Introduction 102 4.3.2 Hybridization 103 4.3.3 Matrices and Determinants 108 4.3.4 The Simple Huckel Method-Theory 118 4.3.5 The Simple Huckel Method—Applications 133 4.3.6 Strengths and Weaknesses of the Simple Huckel Method 144 4.3.7 The Determinant Method of Calculating the Hiickel cs and Energy Levels 146 4.4 The Extended Hiickel Method 152 4.4.1 Theory 152 4.4.2 An Illustration of the EHM: the Protonated Helium Molecule160 4.4.3 The Extended Hiickel Method-Applications 163 4.4.4 Strengths and Weaknesses of the Extended Hiickel Method 164 4.5 Summary 165 References 168 Easier Questions 172 Harder Questions 175 5 Ab initio Calculations 175 5.1 Perspective 176 5.2 The Basic Principles of the Ab initio Method 176 5.2.1 Preliminaries 177 5.2.2 The Hartree SCF Method 181 5.2.3 The Hartree-Fock Equations 232 5.3 Basis Sets 233 5.3.1 Introduction 238 5.3.2 Gaussian Functions; Basis Set Preliminaries; Direct SCF 255 5.3.3 Types of Basis Sets and Their Uses 255 5.4 Post-Hartree-Fock Calculations: Electron Correlation 261 5.4.1 Electron Correlation 269 5.4.2 The M0ller-Plesset Approach to Electron Correlation 281 5.4.3 The Configuration Interaction Approach To Electron Correlation - The Coupled Cluster Method 291 5.5 Applications of the Ab initio Method 332 5.5.1 Geometries 337 5.5.2 Energies 359 5.5.3 Frequencies and Vibrational Spectra 364 5.5.4 Properties Arising from Electron Distribution: Dipole Moments, Charges, Bond Orders,Electrostatic Potentials, Atoms-in-Molecules (AIM) 372 5.5.5 Miscellaneous Properties - UV and NMR Spectra, Ionization Energies, and Electron Affinities 372 5.5.6 Visualization 372 5.6 Strengths and Weaknesses of Ab initio Calculations 373 5.6.1 Strengths 373 5.6.2 Weaknesses 374 5.7 Summary 375 References 388 Easier Questions 388 Harder Questions389 6 Semiempirical Calculations 391 6.1 Perspective 391 6.2 The Basic Principles of SCF Semiempirical Methods 393 6.2.1 Preliminaries 393 6.2.2 The Pariser-Parr-Pople (PPP) Method 396 6.2.3 The Complete Neglect of Differential Overlap (CNDO) Method 398 6.2.4 The Intermediate Neglect of Differential Overlap (INDO) Method 399 6.2.5 The Neglect of Diatomic Differential Overlap (NDDO) Methods 400 6.3 Applications of Semiempirical Methods 412 6.3.1 Geometries 412 6.3.2 Energies 419 6.3.3 Frequencies and Vibrational Spectra 423 6.3.4 Properties Arising from Electron Distribution: Dipole Moments, Charges, Bond Orders 426 6.3.5 Miscellaneous Properties - UV Spectra, Ionization Energies,and Electron Affinities 431 6.3.6 Visualization 434 6.3.7 Some General Remarks 435 6.4 Strengths and Weaknesses of Semiempirical Methods 436 6.4.1 Strengths 436 6.4.2 Weaknesses 436 6.5 Summary 437 References 438 Easier Questions 443 Harder Questions 443 7 Density Functional Calculations 445 7.1 Perspective 445 7.2 The Basic Principles of Density Functional Theory 447 7.2.1 Preliminaries 447 7.2.2 Forerunners to Current DFT Methods 448 7.2.3 Current DFT Methods: The Kohn-Sham Approach 449 7.3 Applications of Density Functional Theory 467 7.3.1 Geometries 468 7.3.2 Energies 477 7.3.3 Frequencies and Vibrational Spectra 484 7.3.4 Properties Arising from Electron Distribution-Dipole Moments, Charges, Bond Orders, Atoms-in-Molecules 487 7.3.5 Miscellaneous Properties-UV and NMR Spectra,Ionization Energies and Electron Affinities,Electronegativity, Hardness, Softness and the Fukui Function 491 7.3.6 Visualization 509 7.4 Strengths and Weaknesses of DFT 509 7.4.1 Strengths 509 7.4.2 Weaknesses 510 7.5 Summary 510 References 512 Easier Questions 518 Harder Questions 518 8 Some “Special” Topics: Solvation, Singlet Diradicals,A Note on Heavy Atoms and Transition Metals 521 8.1 Solvation 521 8.1.1 Perspective 522 8.1.2 Ways of Treating Solvation 535 8.2 Singlet Diradicals 535 8.2.1 Perspective 537 8.2.2 Problems with Singlet Diradicals and Model Chemistries 547 8.2.3 (1) Singlet Diradicals: Beyond Model Chemistries.(2) Complete Active Space Calculations (CAS) 547 8.3 A Note on Heavy Atoms and Transition Metals 548 8.3.1 Perspective 549 8.3.2 Heavy Atoms and Relativistic Corrections 550 8.3.3 Some Heavy Atom Calculations 552 8.3.4 Transition Metals 553 8.4 Summary 558 References 558 Solvation 558 Easier Questions 558 Harder Questions 558 Singlet Diradicals 559 Easier Questions 559 Harder Questions 559 Heavy Atoms and Transition Metals 560 Easier Questions 561 Harder Questions 561 9 Selected Literature Highlights, Books, Websites, Software and Hardware 561 9.1 From the Literature 566 9.1.1 Molecules 568 9.1.2 Mechanisms 572 9.1.3 Concepts 572 9.2 To the Literature 576 9.2.1 Books 577 9.2.2 Websites for Computational Chemistry in General 578 9.3 Software and Hardware 577 9.3.1 Software 577 9.3.2 Hardware 581 9.3.3 Postscript 582 References 582 Answers 585 Index 655
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